Collision Dynamics: what happens when a moving car is rear-ended?

Physics2Collision Dynamics: Dissecting Impact, by Angela Stacey

(Physics disclaimer: Assuming ideal conditions, friction out of scope, assuming no loses to H/L/S, decel/accel out of scope).


It’s the moment we CPST’s fear most. Impact from a vehicular collision. And rightfully so! A lot goes on in the milliseconds leading up to, during and after an impact. But by growing our understanding of how these timeframes play out, we can help to better protect the occupants of our vehicles and those of the families we help. And hey, physics is fun! (Don’t believe me? You’ll see).

First, let’s start with some basic physics: Newton’s Laws of Motion. Not a math lover? Never been one for complex equations? Well, you’re in luck, Newton’s Laws are simple to interpret and apply to everyday situations. These three laws govern the motion of anything and everything, including your vehicle. These laws will be the main tool in our impact dissection kit, so let’s take a look at them.

Laws of PhysicsFirst law: Every object in a state of uniform motion or at rest will remain at rest or in uniform motion in a straight line unless acted upon by an external force.

Second law: The relationship between an object’s mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (meaning they have both a magnitude and a direction).

Third law: For every action there is an equal and opposite reaction. That is, when one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Not so bad, right?

Let’s put ourselves at the scene of a rear-end collision. For simplicity, we’ll say that they are both the same model of vehicle, with the same mass*. We have been told that the vehicle traveling behind (a silver vehicle) has impacted the vehicle in front (a blue vehicle) as the pair were coming to a stop at a red light. No one is badly injured, but both drivers seek to better understand why their necks hurt.

In order to better understand what happens in a collision at the moment of impact, we must first look at what happens before that moment. Our bodies, our children and our trunk full of groceries are all traveling at the same speed as the vehicle. Now would be an excellent time to read Newton’s First law of motion again. Go ahead, I’ll wait.

The objects in your vehicle are traveling in a state of (relatively) uniform motion in the moments before the impact. They will carry on that way until…something acts to stop them or change their course. The silver vehicle impacting the blue vehicle serves this function. As the vehicles impact one another, the contents of the vehicles impact the surfaces adjacent to them. The force with which objects contact one another is equal to the product of the mass of the object (in kilograms) and the acceleration of the object (in m/s2 ), which is Newton’s second law: F = ma. I will point out that units are very, very important!

So that bottle of windshield wash in the foot well of your vehicle? It’s time to put that in the trunk to make sure it doesn’t continue in uniform motion and impact someone in the event of a collision!

At the moment of impact, everything (and everyone) moves toward the point of impact. Give Newton’s third law another read. In a collision between two objects, both objects experience forces that are equal in magnitude but opposite in direction. The person in the silver vehicle will feel a force “coming back” to them that is equal to the force they hit the blue vehicle with, but again, in the opposite direction. This is why the person in the rear vehicle will move forward in their primary post-impact movement, and the person in the front vehicle will move backward, pressing into their seat. Occupants of both vehicles will move toward the point of impact because of the equal and opposite forces described by Newton’s third law. Take silver vehicle’s force to be directed –> this way, then the blue vehicle’s force would be equal and oppositely directed <– this way. Giving you: S–> <–B

Rear end collisions also involve the consideration that both vehicles are moving in the same direction, though one has unfortunately “caught up” with the other. This affects the outcome such that both vehicles will continue to move along that path until they come to a stop, their original direction of travel being the same means that their force vectors (think of these as arrows that represent the direction the vehicle is moving, with a length proportional to the mass multiplied by the acceleration of the vehicle) will add. Yet another reason why rear end collisions do not represent a large amount of overall collision injuries.

A video may help, see above: (silver vehicle = silver bottle, blue vehicle = blue bottle)

I hope that this short explanation has helped to increase your understanding of the basic physics of a collision, and will serve as a motivation to learn more about physics!

*Something to note: In accordance with Newton’s second law of motion, the acceleration of an object is dependent upon both force and mass. Thus, if the colliding objects have unequal mass, they will have unequal accelerations (or rather, decelerations) as a result of the contact force that results during the collision. This is why you will see a small car slide across the road when hit by a Hummer. Mass is (sometimes unfortunately) directly related to force.